Background: There are few studies investigating the relationship between respiratory viral infection in pregnancy and asthma in the offspring, and none among mothers with asthma. Infants of mothers with asthma are more likely to wheeze and have a higher risk of developing asthma than infants of non-asthmatic mothers. Methods: A prospective cohort study of viral infection in pregnancy was conducted between 2007 and 2009, and a subgroup of infants of mothers with asthma was followed up at 6 and 12 months of age. During common colds, nasal and throat swabs were collected from mothers and respiratory viruses detected by polymerase chain reaction. Respiratory health of infants was assessed by parent-completed questionnaire. Results: Twelve-month-old infants whose mothers had confirmed viral infections in pregnancy (n = 26) reported more frequent wheeze (40% had 4–12 wheeze attacks compared with 0%), sleep disturbed by wheeze (1 night per week or more in 60% vs. 11%), beta agonist treatment for wheeze (27% vs. 0%), prolonged colds (2 wk or longer 31% vs. 0%), more eczema (40% vs. 6.3%), and parent-perceived asthma (32% vs. 0%), compared with infants whose mothers had common colds without laboratory-confirmed viral infection (n = 16). Conclusions: This study demonstrates a relationship between maternal respiratory viral infection in pregnancy and wheezing illness in infants of mothers with asthma. Viral infections are the most common cause of asthma exacerbations in pregnancy, and infants of asthmatic mothers are at increased risk of asthma themselves. Further research is needed to elucidate the mechanisms involved.